I had a similar issues for the past few months with Freya 0.3.1. This was the final step in my repairs. The steps I did to finally resolve this issue was edited these files (take the time to make backups of each of these before starting these steps):

sudo mc

--->navigate to each of these files & using "F4">then editing the following files>CTRL+X>Y>keep file name the same.

--->File list

-> /etc/apt/sources.list
--->added (for some reason they were deleted)
--->
#### Elementary PPA - hxxp://www.elementaryos.com
deb hxxp://ppa.launchpad.net/elementary-os/os-patches/ubuntu trusty main
deb hxxp://ppa.launchpad.net/elementary-os/daily/ubuntu trusty main
deb hxxp://ppa.launchpad.net/elementary-os/testing/ubuntu trusty main

-> /etc/apt/sources.list.d/elmentary.list
--->removed # (both lines were commented out)

deb hxxp://ppa.launchpad.net/elementary-os/stable/ubuntu trusty main
deb-src hxxp://ppa.launchpad.net/elementary-os/stable/ubuntu trusty main

-> /etc/ls-release

--->replaced (for some reason had been changed to Ubuntu 14.04) ---->

DISTRIB_ID=Ubuntu

DISTRIB_RELEASE=14.04

DISTRIB_CODENAME=trusty

DISTRIB_DESCRIPTION="Ubuntu 14.04 LTS"

----Changed to reflect Elementary OS Freya

DISTRIB_ID="elementary OS"

DISTRIB_RELEASE=0.3.1

DISTRIB_CODENAME=freya

DISTRIB_DESCRIPTION="elementary OS Freya"

-> /etc/os-release 

--->replaced (for some reason had been changed to Ubuntu 14.04)---->

NAME="Ubuntu"

VERSION="14.04.1 LTS, Trusty Tahr"

ID=ubuntu

ID_LIKE=debian

PRETTY_NAME="Ubuntu 14.04.1 LTS"

VERSION_ID="14.04"

HOME_URL="hxxp://www.ubuntu.com/"

SUPPORT_URL="hxxp://help.ubuntu.com/"

BUG_REPORT_URL="hxxp://bugs.launchpad.net/ubuntu/"

---->Changed to reflect Elementary OS Freya

NAME="elementary OS"

VERSION="0.3.2 Freya"

ID="elementary OS"

ID_LIKE=ubuntu

PRETTY_NAME="elementary OS Freya"

VERSION_ID="0.3.1"

HOME_URL="hxxp://elementary.io/"

SUPPORT_URL="hxxp://elementary.io/support/"

BUG_REPORT_URL="hxxps://bugs.launchpad.net/elementary/+filebug"

(You must replace hxxp with http, due to site restrictions. Also files ls-release & os-release should not have spaces, the site bunched the information, so I added the spaces to make this post easier to read)

Then I followed the steps here:
sudo apt-get update
sudo apt-get -f install
sudo apt-get dist-upgrade
sudo apt-get install --reinstall humanity-icon-theme elementary-icon-theme

Now my Software Center works as it should. Hope this helps others and saves a great amount of time.


<<<<WARNING>>>>
You can potential bork your entire system. I do not recommend attempting this repair without feeling comfortable with using the command line.